Question

1.A hospital spokesperson reported that 4 births had taken place at the RG Hospital during the last 24 hours. Find the following probabilities:

a.P(A) = that 2 boys and 2 girls are born.

b.P(B) = no boys are born.

c.P(C) = at least one boy is born.

2.The odds that a team will win in the finals is 4:3. What is their chance of winning?

3.The probability that a patient entering RG Hospital will consult a physician is 0.7, that he/she will consult a dentist is 0.5 and that he/she will consult a physician or a dentist or both is 0.9. What is the probability that a patient entering the hospital will consult both a physician and a dentist?

Answer 1

Note : Allowed to solve one question per post. However, solved all the question.

.A hospital spokesperson reported that 4 births had taken place at the RG Hospital during the last 24 hours. Find the following probabilities:

a.P(A) = that 2 boys and 2 girls are born.

b.P(B) = no boys are born.

c.P(C) = at least one boy is born.

The probability of a boy or girl being born is equal hence it 0.50
Hence we in case of 4 birth, we have 16 different possible combination
(B,   B,   B,   B)
(G,   B,   B,   B)
(B,   G,   B,   B)
(G,   G,   B,   B)
(B,   B,   G,   B)
(G,   B,   G,   B)
(B,   G,   G,   B)
(G,   G,   G,   B)
(B,   B,   B,   G)
(G,   B,   B,   G)
(B,   G,   B,   G)
(G,   G,   B,   G)
(B,   B,   G,   G)
(G,   B,   G,   G)
(B,   G,   G,   G)
(G,   G,   G,   G)

a.P(A) = that 2 boys and 2 girls are born.

Hence we have 2B and 2G , in 6 combination
(G,   G,   B,   B)
(G,   B,   G,   B)
(B,   G,   G,   B)
(G,   B,   B,   G)
(B,   G,   B,   G)
(B,   B,   G,   G)

P(A) = 6/16 = 3/8

b.P(B) = no boys are born.

In this case we have 1 combination
(G,   G,   G,   G)

P(B) = 1/16

c.P(C) = at least one boy is born.

P(C) = 1 - P(no boys are born) = 1- (1/16) = 15/16

The odds that a team will win in the finals is 4:3. What is their chance of winning?

Here the odds of winning is 4:3
It means that you win 4 matches for every 3 matches you lose.
Hence the team wins 4 matches about 7

probability of winning= 4/7

3.The probability that a patient entering RG Hospital will consult a physician is 0.7, that he/she will consult a dentist is 0.5 and that he/she will consult a physician or a dentist or both is 0.9. What is the probability that a patient entering the hospital will consult both a physician and a dentist?

P(Physcian) = P(Phy) = 0.7
P(Dentist) = P(Den) = 0.5
P(Phy U Den) = 0.9

P(Phy n Den) = ?

P(Phy U Den)=P(Phy)+P(Den)-P(Phy n Den)

P(Phy n Den)= 0.7+0.5-0.9= 0.3